Some gas turbine engines operate at temperatures which are such as to require that at least some parts of its turbine apparatus be provided with appropriate supplies of cooling air from the engine compressor. However, air taken from the compressor for turbine cooling reduces the amount available for burning in the combustion system, thus generating an engine performance penalty. That situation is further exacerbated in that the air lost to the combustion system through cooling needs, adds to air lost through unavoidable leakage thereof through seals between the static and rotating members that make up the compressor assembly, the leaked air passing into the space volume bounded by the combustion apparatus and turbine shafts.